A083738 Pseudoprimes to bases 2,3 and 7.
1105, 2465, 10585, 18721, 29341, 46657, 75361, 104653, 115921, 162401, 226801, 252601, 278545, 294409, 314821, 334153, 340561, 399001, 410041, 449065, 488881, 512461, 530881, 534061, 552721, 574561, 658801, 721801, 852841, 1024651
Offset: 1
Examples
a(1)=1105 since it is the first number such that 2^(k-1) = 1 (mod k), 3^(k-1) = 1 (mod k) and 7^(k-1) = 1 (mod k).
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10460 (terms 1..98 from R. J. Mathar)
- F. Richman, Primality testing with Fermat's little theorem
Crossrefs
Intersection of A001567 and A083735. Intersection of A005935 and A083733. - R. J. Mathar, Apr 05 2011
Programs
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Mathematica
Select[Range[1, 10^5, 2], CompositeQ[#] && PowerMod[2, #-1,#] == PowerMod[3, #-1,#] == PowerMod[7, #-1,#] == 1&] (* Amiram Eldar, Jun 29 2019 *)
Formula
a(n) = n-th positive integer k(>1) such that 2^(k-1) = 1 (mod k), 3^(k-1) = 1 (mod k) and 7^(k-1) = 1 (mod k).